The rotation of the Earth (of radius R) about | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that,the angle of latitude is $\lambda = 45^{\circ}$.The effective acceleration due to gravity at a latitude $\lambda$ is given by $g_{\lamb

Vedclass · Accepted Answer

$\pi \sqrt{\frac{2 R}{g}}$

Vedclass · Answer

(B) Given that,the angle of latitude is $\lambda = 45^{\circ}$.The effective acceleration due to gravity at a latitude $\lambda$ is given by $g_{\lambda} = g - \omega^2 R \cos^2 \lambda$.The apparent weight of a man of mass $m$ at this point is $w = m g_{\lambda} = m(g - \omega^2 R \cos^2 \lambda)$.According to the question,the man feels weightlessness,so $w = 0$.Therefore,$m(g - \omega^2 R \cos^2 45^{\circ}) = 0$.Since $m 
eq 0$,we have $g - \omega^2 R (\frac{1}{\sqrt{2}})^2 = 0$,which simplifies to $g - \frac{\omega^2 R}{2} = 0$.This gives $\omega^2 = \frac{2g}{R}$,or $\omega = \sqrt{\frac{2g}{R}}$.The duration of a day (time period $T$) is given by $T = \frac{2\pi}{\omega}$.Substituting the value of $\omega$,we get $T = \frac{2\pi}{\sqrt{2g/R}} = 2\pi \sqrt{\frac{R}{2g}} = \pi \sqrt{\frac{2R}{g}}$.

The rotation of the Earth (of radius $R$) about its axis speeds up to a value such that a man at latitude angle $45^{\circ}$ feels weightlessness. The duration of a day in such a case is

Similar Questions

The variation of acceleration due to gravity $(g)$ with distance $(r)$ from the center of the earth is correctly represented by ... (Given $R =$ radius of earth)

$A$ body weighs $49 \, N$ on a spring balance at the North Pole. What will be its weight recorded on the same weighing machine if it is shifted to the equator (in $, N$)? (Use $g = \frac{GM}{R^2} = 9.8 \, m/s^2$ and radius of the Earth,$R = 6400 \, km$.)

Two spherical planets $A$ and $B$ have the same mass,but their densities are in a ratio $8:1$. For these planets,the ratio of acceleration due to gravity at the surface of $A$ to its value at the surface of $B$ is:

The weight of a body of mass $m$ decreases by $1\%$ when it is taken to a height $h$ above the surface of the Earth. What is the percentage decrease in its weight when it is taken to a depth $h$ below the surface of the Earth?

If $R_{E}$ is the radius of the Earth,then the ratio between the acceleration due to gravity at a depth $r$ below and a height $r$ above the Earth's surface is: (Given: $r < R_{E}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module